Tensor
networks states describe many-body quantum systems with local
interactions in thermal equilibrium. At zero temperature, they
correspond to ground states of frustration-free local Hamiltonians,
and fulfill the so-called area law: the entropy of the reduced state
corresponding to a connected region scales with the area surronding
that region, and not with its volume. This indicates that there
should be a holographic map between the bulk and the boundary of any
connected region. We derive such a map, and show how the bulk
properties of the state can be obtained from a theory that lives at
the boundary, described by a boundary Hamiltonian. For gapped
systems, that Hamiltonian is local and becomes non-local as one
approaches a gapless phase. For topological phases, the Hamiltonian
can be splitted into a universal one, which is constant in the whole
phase, and a local Hamiltonian which depends on the microscopic
details.